enigma - i think she will pick english up very quickly and not forget polish.
I grew up in Malaysia speaking 3 different languages. My parents spoke Tamil and English at home and we learnt Malay in school as the main medium.
Along the way, somehow my brother and I ended up speaking more English at home than Tamil though our parents still speak to us in both languages and we can read and write and watch Tamil programs. I think that's what you don't want to happen to your daughter.
My parents kinda let go but when they wanted us to speak more Tamil we were at the stage where English was more comfortable and being teenagers didn't want to change. This I really regret now. My spoken Tamil can be better.

I don't remember how we picked up Malay, my parents spoke little with the neighbours etc. But we must have picked it up before we went to school from the kids in the neighbourhood.
And because Malaysia is a multicultural country, we also picked up other languages like Mandarin and Cantonese from our school friends.

So, I'm pretty sure Aneta will pick up English in no time, but yeah, if she has constant Polish at home, it will be no problem. She will be thinking in different languages.
When I speak different languages I think in those languages, because they are so inherent.
But now when I try to learn a new language, I'm translating them in my head from English.

Hope this helps